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Abstract

In this paper, we present a continuous approach to ordering 2D images when compositing. Previous methods for
stacking image layers require them to appear in a single (though possibly different) order at every point in the
image. Our soft stacking approach removes this restriction – allowing layers to stack as if they were volumes of fog,
appearing partially in front of and partially in back of other layers within the same pixel, and moving smoothly
through other layers across the image. Our approach involves augmenting each pixel with stacking coefﬁcients
– a necessary and sufﬁcient representation for sub-pixel stacking complexity. These stacking coefﬁcients arise
naturally when considering sub-pixel stacking complexity, much as continuous (alpha) transparency arises when
considering sub-pixel coverage complexity.
While the number of stacking coefﬁcients required to represent all possible sub-pixel stacking arrangements is
factorial in the number of layers in the stack, in many practical situations only a small subset of the stacking
coefﬁcients are nonzero. We use this sparsity as the basis of a prototype that allows artists to interactively paint
stacking adjustments into composites. Additionally, we demonstrate how to generate optimally-stacked images
under a generalized notion of stacking consistency.